From: pat hayes <phayes@ai.uwf.edu>

Date: Fri, 28 Feb 2003 12:13:46 -0700

Message-Id: <p05111b11ba8557386af9@[10.0.100.86]>

To: herman.ter.horst@philips.com

Cc: www-rdf-comments@w3.org

Date: Fri, 28 Feb 2003 12:13:46 -0700

Message-Id: <p05111b11ba8557386af9@[10.0.100.86]>

To: herman.ter.horst@philips.com

Cc: www-rdf-comments@w3.org

> >..... >>> >>The semantic conditions on rdfs:range and rdfs:domain in Section 3.3 >>>>>do not yet incorporate explicit domain assumptions as just >>>>>discussed. It seems that additions such as the following need >>>>>therefore to be made: >>>> >>>>The additions suggested are not required, since they follow from the >>>>axiomatic triples in the next table and the other conditions on range >>>>and domain. >>>> >>>>It is probably easiest to express the reasoning in terms of triples >>>>that must be satisfied by an interpretation I. For example, suppose >>>><x,y> is in IEXT(I(rdfs:range)), ie that >>>> >>>>I |= (x) rdfs:range (y) >>> >>>I do not understand this step. In these two lines x/y have a different >>>origin. In "<x,y> is in IEXT(I(rdfs:range))", x and y are in IR. >>>In the triple "(x) rdfs:range (y)", x and y are uri's or blank nodes >>>(y may also be a literal). So this conclusion ("ie that") >>>is not clear. >> >>Sorry, I was using an unstated convention. Let me rephrase it more >carefully. >> >>Suppose <x,y> is in IEXT(I(rdfs:range)) and suppose that I(aaa)=x and >>I(bbb)=y. Then >> >>I |= aaa rdfs:range bbb . >> >>Now, since >> > >I |= rdfs:range rdfs:domain rdf:Property . (axiomatic triple) >> >>it follows by the semantic conditions on rdfs:domain that >> >>I |= aaa rdf:type rdf:Property . >> >>and hence that I(aaa)=x is in IP. >> >>Similarly for bbb, the axiomatic triple defining the range of >>rdfs:range, and IC. >> >>Pat > >Pat, thank you for the explanation. >You now introduce in the proof an additional assumption. No, this is only an assumption of the way I presented the argument in the email. Let me rephrase the argument in full without trying to shorten it: First, the truth of the axiomatic triple rdfs:range rdfs:domain rdf:Property . and the semantic conditions on rdfs:domain together require that <x,y> inIEXT(I(rdfs:range)) implies x in ICEXT(I(rdf:Property)) which in turn, by applying the condition (definition if you like :) IP= ICEXT(I(rdf:Property)) means that <x,y> in IEXT(I(rdfs:range)) implies x in IP Similarly y is in IC, using a different axiomatic triple. Is this more convincing? -Pat >What you prove is the following: > If <x,y> is in IEXT(I(rdfs:range)) > AND IF x and y are in the range of the function IS > then x is in IP and y is in IC. >However, this statement does not suffice: the additional >assumption (AND IF ...) would need to be dropped. >However, I believe that it is not possible to prove that > If <x,y> is in IEXT(I(rdfs:range)) > then x is in IP and y is in IC >(and similarly for rdfs:domain). > >Therefore, my remark remains. >Let me recall in a slightly rephrased manner what I said in >the first mail in this thread: > >For each occurrence of IEXT(x) or ICEXT(x), it >should be clear that x is in the domain of the function >involved. (For IEXT, this domain is the set IP. >For ICEXT, the domain is the set IC, as you have now confirmed.) >For example, in Section 3.3 the semantic conditions on >subClassOf and subPropertyOf take care of this explicitly. > >The semantic conditions on rdfs:range and rdfs:domain in Section 3.3 >do not yet incorporate explicit domain assumptions as just >discussed. It seems that additions such as the following need >therefore to be made: > > If <x,y> is in IEXT(I(rdfs:range)) > [then x is in IP and y is in IC] and > [if, in addition,] <u,v> is in IEXT(x) then > v is in ICEXT(y) > > If <x,y> is in IEXT(I(rdfs:domain)) > [then x is in IP and y is in IC] and > [if, in addition,] <u,v> is in IEXT(x) then > u is in ICEXT(y) > >>-- >>--------------------------------------------------------------------- >>IHMC (850)434 8903 or (650)494 3973 home >>40 South Alcaniz St. (850)202 >4416 office >>Pensacola (850)202 4440 fax >>FL 32501 (850)291 0667 cell >>phayes@ai.uwf.edu http://www.coginst.uwf.edu/~phayes >>s.pam@ai.uwf.edu for spam >> >> > >Herman -- --------------------------------------------------------------------- IHMC (850)434 8903 or (650)494 3973 home 40 South Alcaniz St. (850)202 4416 office Pensacola (850)202 4440 fax FL 32501 (850)291 0667 cell phayes@ai.uwf.edu http://www.coginst.uwf.edu/~phayes s.pam@ai.uwf.edu for spamReceived on Friday, 28 February 2003 14:13:50 GMT

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